Question:
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is
The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_1y = (c_2 +c_3 )e^{x+c_4}$ is
Updated On: May 22, 2024
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The Correct Option is A
Solution and Explanation
$\left(y = [(\frac{C_2 + C_3}{C_1})e^{C_4}]e^x = A e^x,\right)$
where $A = \left((\frac{C_2 + C_3}{C_1})e^{C_4}\right)$
Order = Number of independent arbitrary constants $= 1$
where $A = \left((\frac{C_2 + C_3}{C_1})e^{C_4}\right)$
Order = Number of independent arbitrary constants $= 1$
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Concepts Used:
Order and Degree of Differential Equation
The equation that helps us to identify the type and complexity of the differential equation is the order and degree of a differential equation.
The Order of a Differential Equation:
The highest order of the derivative that appears in the differential equation is the order of a differential equation.
The Degree of a Differential Equation:
The highest power of the highest order derivative that appears in a differential equation is the degree of a differential equation. Its degree is always a positive integer.
For examples:
- 7(d4y/dx4)3 + 5(d2y/dx2)4+ 9(dy/dx)8 + 11 = 0 (Degree - 3)
- (dy/dx)2 + (dy/dx) - Cos3x = 0 (Degree - 2)
- (d2y/dx2) + x(dy/dx)3 = 0 (Degree - 1)